Electroweak Symmetry Breaking

Home , Electroweak scale

High Energy Physics has established that all known natural phenomena can be described by a Beyond the Standard Model local quantum ﬁeld theory which is invariant under:

3+1 dimensional Lorentz transformations SO(3, 1) and translations • Bogdan Dobrescu (Fermilab) SU(3) SU(2) U(1) gauge transformations • C × W × Y = all elementary particles belong to certain Outline: ⇒ representations of the Lorentz and gauge groups: Electroweak symmetry breaking (Lecture 1) • Spin-1 bosons Spin-1/2 fermions Quark and lepton masses; vectorlike quarks (Lecture 2) • New gauge bosons (Lecture 3) qL :(3, 2, +1/6) • Gµ :(8, 1, 0) u :(3, 1, +2/3)  R WIMPs and cascade decays (Lecture 4) W µ :(1, 3, 0) 3 d :(3, 1, 1/3) •  ×  R − Bµ :(1, 1, 0)  l :(1, 2, 1/2) How to search for new phenomena (Lecture 5)   L − • eR :(1, 1, 1)   −  September 2011 - European School of HEP  Spin-2: graviton Dark matter particle (spin =?) . 1.1 .

Electroweak symmetry breaking High Energy Physics has established that all known natural phenomena can be described by a We know that SU(2) U(1) U(1) local quantum ﬁeld theory which is invariant under: W × Y → Q 3+1 dimensional Lorentz transformations SO(3, 1) and translations W and Z have not only transverse polarizations, • ⇒ ± SU(3) SU(2) U(1) gauge transformations • C × W × Y but also longitudinal ones: three spin-0 states have = all elementary particles belong to certain been eaten. ⇒ representations of the Lorentz and gauge groups: What is the origin of EWSB? Spin-1 bosons Spin-1/2 fermions We don’t know: qL :(3, 2, +1/6) µ + G :(8, 1, 0) uR :(3, 1, +2/3) what unitarizes W W scattering? µ  L L− W :(1, 3, 0) 3  dR :(3, 1, 1/3) •  µ ×  −  B :(1, 1, 0)  lL :(1, 2, 1/2) e :(1, 1, −1) why is there a VEV that breaks SU(2) U(1) ? R − • ×     what has a VEV that breaks SU(2) U(1) ? Spin-2: graviton Dark matter particle (spin =?) • ×

. . 1.4 Electroweak symmetry breaking + WL WL− scattering: We know that SU(2) U(1) U(1) W × Y → Q W and Z have not only transverse polarizations, ⇒ ± 2 but also longitudinal ones: three spin-0 states have Perturbatively: + + GF s σ W W − W W − L L → L L ≈ 16π been eaten. % & This makes sense only up to √s 1 TeV (see Lecture 5 of E. Dudas). ∼ What is the origin of EWSB? At higher energy scales: We don’t know: # A new particle: Higgs boson + what unitarizes W W − scattering? • L L OR # New strong interactions (perturbative expansion breaks down) why is there a VEV that breaks SU(2) U(1) ? • × OR what has a VEV that breaks SU(2) U(1) ? • × # Quantum ﬁeld theory description breaks down

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Alternative to Higgs boson: spin-1 particles (ρT ) coupled to WW.

Homework 1.1 Unitarity in WW scattering may be restored by ρT exchange.

Draw the Feynman diagrams for WW WW and WZ WZ in → → However, ρT ρT and ρT W scattering are then non-unitary, unless the standard model which are relevant in the M M limit. h ( W some other particles exist. Devise experimental searches for the Higgs boson using thesepro- cesses. a whole tower of heavy particles is needed .... it sounds like → QCD, but at a scale 103 higher! Hint: the LHC is not only a gg or gq or qq collider, but also a WW and a WZ collider! “Technicolor”: a new gauge interaction which becomes strong at the TeV scale.

Techni-fermion condensate breaks electroweak symmetry (same . 1.7 as chiral symmetry breaking in QCD).

ρT is the techni-rho.

. 1.8 Searches for the standard-model Higgs boson:

Technicolor has problems with the ﬁts to the electroweak ob- SM ATLAS Preliminary CLs Limits ! / servables. However, strongly coupled ﬁeld theories are poorly ! Observed Expected understood, so it is hard to make precise predictions. Ldt = 1.0-2.3 fb-1 10 ± 1 ! " ± 2 ! s = 7 TeV 95% CL Limit on on Limit CL 95% Another example of spin-1 particles that unitarize WW scatter- 1 ing: Kaluza-Klein modes in a model with one extra dimension

where the electroweak symmetry is broken by boundary condi- -1 10 200 300 400 500 600 tions: mH [GeV]

”Higgsless models” Csaki, Grojean, Pilo, Terning: hep-ph/0308038 Tevatron Run II Preliminary, L # 8.6 fb-1 LEP Exclusion Tevatron lightest spin-1 resonances around 1.2 TeV 10 Exclusion Expected → Observed ±1! Expected ±2! Expected Room for SM Higgs boson has shrank dramatically this

1.9 95% CL Limit/SM . 1 summer! SM=1 1.10 . Tevatron Exclusion July 17, 2011 100 110 120 130 140 150 160 170 180 190 200 2 mH(GeV/c )

Hidding the Higgs boson Hidding the Higgs boson

SM gluon fusion SM gluon fusion non-standard production ± g . ? h0 ? g g t t g ? h0 h0 t t g ? t t g g h0

g ?

The cross section for gluon fusion may be reduced, but only if there are new colored particles at the electroweak scale.

. 1.12 SM Exp. Obs. Exp. Obs. Nonstandard Higgs decays: a case study

! -1 -1 -1 -1

/ H% $$ H (1.08% $$ (1.08 fb ) fb ) H% ZZH% ZZ llll% (1.96-2.28llll (1.96-2.28 fb fb) ) -1 -1 -1 -1 ! H% WWH%% WW l&%l& l & (1.70l& (1.70 fb fb) ) H% ZZH% ZZ llqq% llqq (1.04 (1.04 fb fb) ) -1 -1 W/Z H,W/Z H %H, Hbb % bb(1.04 (1.04 fb -1fb) ) H% ZZH% ZZ ll&%& ll (1.04&& (1.04 fb-1 fb) ) -1 -1 H% '' H %(1.06'' (1.06 fb )fb ) Standard model + a scalar singlet S: cH†HS†S

1 iA0/ S 0 10 S = (ϕS + S ) e ) * , A is a CP-odd spin-0 particle (axion) √2 ) *

1/2 cv c2 v2 M 2 95% CL limit on h0A0A0 coupling Γ(h0 A0A0)= 1 4 A ⇒ → − 2 2 32πMh ' Mh ( 1

-1 ATLAS Preliminary " L dt ~ 1.0-2.3 fb , s=7 TeV CLs limits 100 200 300 400 500 600 Dobrescu, Landsberg, Matchev, hep-ph/0005308 mH [GeV] Homework 1.2: What other channels can be used? . 1.14

. 1.13

0 B(A γγ) 3 If χ is both colored and electrically charged: → 10− . The subsequent decays of A0 are model dependent. B(A0 gg) ≈ → h A0A0 (γγ)(jj) may be the most interesting decay, with → → Example: = ξSχLχR +h.c. V (H, S) , χ is a new fermion the diphoton and dijet peaks having same mass. (Chang, Fox, Weiner, L − hep-ph/0608310, ... )

γ γ (g) χ g y 0 A0 A χ h0 γ χ y γ (g) g A0 g

y g Eﬀective coupling of the axion to pairs of gluons and photons: √ 2 0 µνρσ 2 − A ) T2(χ)αs GµνGρσ + Nce α FµνFρσ Homework 1.3: 16π S χ ) * ) * Draw the Feynman diagrams for pp Wh W γγjj. → → Roughly estimate the LHC cross section for this signal and identify the . 1.15 main backgrounds. (Hint: see A. Martin, hep-ph/0703247)

. 1.16 Hierarchy problem For a light A0, this may appear in the detector as h A0A0 (γγ)j or h A0A0 “γ” j. → → → → Quantum ﬂuctuations tend to increase the γ g 0 h0 0 A A vacuum expectation value of the Higgs ﬁeld. γ g h, W Homework 1.4: t '$ h '$ h hh Estimate MA such that: a) the jets overlap; b) the photons overlap. &% &% (assume Mh =120GeV)

Stability of the electroweak scale requires a modiﬁca- If χ is electrically-neutral but carries color B(A0 jj) 100% ⇒ → ≈ h A0A0 4j is the main decay mode for M < 2M tion of the standard model at scales above 1 TeV. → → h W ∼ huge background at the LHC, ⇒ Higgs boson will be hard to discover ... (use jet substructure?)

. 1.18 . 1.17

Energy Solution #1: Supersymmetric Standard Model TT

16 No quadratic divergences because loops with superpartners par- 10 TeV quantum gravity tially cancel the SM loops

h, W Dynamical susy t '$ 8 h '$ h hh 10 10 TeV breaking sector &% ∼ − &% t˜ H,˜ W˜ c '$ 7 Messenger sector hhh '$ h 10 10 TeV ? − &% &%

c Additional structures required to explain why H M ,µ. ) *∼ SUSY 1 TeV MSSM ∼ . 1.19

. 1.20 Solution #2: Technicolor Solution #3: A warped extra dimension Energy TT L. Randall, R. Sundrum, hep-ph/9905221

1016 TeV quantum gravity

Technicolor gauge coupling: gTC O(1) ∼ wave function of © graviton 0-mode Planck logarithmic running of gTC “brane” Standard Model % (increases at lower scales, “brane”

just as in QCD) E 0y πyrc z

Interaction of the graviton 0-mode (the massless 4D spin-2 ﬁeld)

c with Standard Model particles is suppressed by its exponentially gTC O(4π) Technifermions condense small wave function at the SM brane. 1 TeV ∼ ⇒ ∼ electroweak symmetry is broken ⇒ Hierarchy between the Planck and electroweak scales is explained!

. 1.21 . 1.22

Solution #4: Composite Higgs models

Higgs boson is a bound state of top quark with a new quark χ. “Top seesaw model” (Chivukula et al, hep-ph/9809470) Scales of RS1 model (measured on the SM brane): Binding may be due to some strongly-interacting heavy gauge bosons

TT Energy χ t

Graviton KK modes are strongly coupled 1 TeV Scale of Higgs compositeness may be as low as a few TeV. ∼ Standard Model Homework 1.5: What are quantum numbers of χ?Howwouldyou search for this hypothetical particle? . 1.23

. 1.24 Solution (?) #5: Large extra dimensions (ADD) (Partial) Solution #6: Little Higgs Graviton only in ﬂat extra dimensions > 3 Gravitational interactions measured at distances 10− cm: 1-loop quadratic divergences cancelled by partners carrying m1m2 ∼ F = the same spin. (Arkani-Hamed et al, hep-ph/0206021) N 2 2 MPlanckr We may live on a wall in extra dimensions! (Arkani-Hamed, Dimopoulos, Dvali, 1998) h, W

t '$ h '$ h hh &% &%

χ H+,W+

'$ '$ hhh h

&% &%

Eﬀective theory valid up to scales of order 5 TeV, where some m1m2 ∼ Newton’s law in extra dimensions: FN = 2+n unspeciﬁed new dynamics takes over. (Msr) 2 1/(2+n) MPlanck Scale of quantum gravity may be as low as 10 TeV: Ms = ∼ Ln 1.26 + , .

. 1.25

(Partial) Solution #7: Twin Higgs Comparison between solutions to the hierarchy problem:

Z. Chacko, H. S. Goh and R. Harnik, hep-ph/0506256 1. Dynamically-broken supersymmetry Susy breaking scale is exponentially suppressed compared to M 1-loop quadratic divergences are cancelled if there is a parity Planck due to gauge dynamics. which interchanges each SM particle with a new particle that transforms under a twin SM gauge group. Problem: µ term (the Higgsino mass) is supersymmetric. Why µ v? (some solutions exist) ∼ If the new particles are neutral under the SM gauge group, than these partners would be very hard to see at the LHC . 2. Technicolor Exponential hierarchy between M and the scale where the tech- ˜ Planck This is unlike all other known solutions, where the a t squark or nicolor gauge interaction becomes strong. a χ quark or something else is visible at the TeV scale. Problem: ﬁt to the electroweak data? (some solutions exist)

Eﬀective theory valid again only up to scales of order 5 TeV... ∼ 3. RS1 . 1.27 1/MPlanck is exponentially suppressed compared to 1/v.

. 1.28 Conclusions to Lecture #1

EWSB argument for new phenomena: unitarity of WLWL scattering requires a Higgs boson or new strong interactions or something more exotic.

Only in the presence of other light new particles it may be hard to discover the Higgs boson at the LHC+Tevatron.

Hierarchy argument for new phenomena: naturalness requires new physics at the TeV scale, but there are many possibilities and it may not be easy to pin down its nature even at the LHC.

Bogdan Dobrescu (Fermilab) - ESHEP - September 2011

. 1.29